Calculate tg 2x , if tg x = 1/3 .

3 Answers | Add Yours

hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

If tg(x)=1/3 , find tg(2x)

We know that: tg(2x)= 2 tg(x)/[1-(tgx)^2

==> tg(2x) = 2(1/3)/[1-(1/3)^2]

                = (2/3)/[1-1/9]

                =(2/3)/(8/9)

                = 2*9/3*8 =  18/24 = 3/4

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

To calculate tg 2x, we'll consider 2x as a sum of 2 identical angles.

tg 2x= tg(x+x)=(tg x+ tg x)/[1-(tgx)^2]

tg 2x=2tg x/[1-(tgx)^2]

We know, from enunciation, that tg x= 1/3.

We'll substitute the value of tg x in the formula for tg 2x.

tg 2x = 2*1/3/(1 - 1/9)

tg 2x = (2/3)*(9/8)

tg 2x =3/4

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

tanx = 1/3. To find tan2x.

We know that tan2x = 2tanx/(1-(tanx)^2) = 2*(1/3)/(1-(1/3)^2) = (2/3) / {1-1/9) = (2/3)/(8/9) = 2*9/(3*8) = 3/4

We’ve answered 318,988 questions. We can answer yours, too.

Ask a question